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# MAA MPP Model | ||
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The Maa microperforate model determines the characteristic impedence $(Z_{c})$ of the layer based on the perforate diameter $(d)$, center-to-center distance $(b)$, and thickness $(t)$. | ||
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Unlike other material models, the Maa MPP model does not calculate a characteristic wavenumber $(k_{c})$. Instead, a separate transfer matrix is used. | ||
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# Determination of Characteristic Impedence | ||
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\[ | ||
Z_{c} = r+j\omega m | ||
\] | ||
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where $r$ is: | ||
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\[ | ||
r = \frac{32\eta t}{\phi d^2} r_{1} | ||
\] | ||
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\[ | ||
r_{1} = \sqrt{1+\frac{x^2}{32}}+\frac{\sqrt{2}}{32} x \frac{d}{t} | ||
\] | ||
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$m$ is: | ||
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\[ | ||
m = \frac{\rho_{0}t}{\phi} m_{1} | ||
\] | ||
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\[ | ||
m_{1} = 1+\frac{1}{\sqrt{1+\frac{x^2}{2}}}+\frac{0.85d}{t} | ||
\] | ||
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and | ||
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\[ | ||
x = \frac{d}{2}\sqrt{\frac{\omega\rho_{0}}{\eta}} | ||
\] | ||
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\[ | ||
\phi = \frac{\pi}{4}\Bigg(\frac{d}{b}\Bigg)^2 | ||
\] | ||
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The characteristic impedence $(Z_{c})$ is then used directly in the layer transfer matrix via the [Add_MAA_MPP_Layer](https://jakep72.github.io/acoustipy/AcousticTMM/#src.acoustipy.TMM.AcousticTMM.Add_MAA_MPP_Layer) method. | ||
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## Model Parameters: | ||
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##### Using the following nomenclature --- Symbol = [Units] (name) | ||
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\[ | ||
d = \Bigg[m\Bigg]\tag{perforate diameter} | ||
\] | ||
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\[ | ||
b = \Bigg[m\Bigg]\tag{center-to-center distance} | ||
\] | ||
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\[ | ||
t = \Bigg[m\Bigg]\tag{layer thickness} | ||
\] | ||
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## Defining Other Symbols: | ||
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##### Using the following nomenclature --- Symbol = [Units] (name) | ||
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\[ | ||
\rho_{0} = \Bigg[\frac{kg}{m^3}\Bigg]\tag{air density} | ||
\] | ||
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\[ | ||
\eta = \Bigg[Pa*s\Bigg]\tag{viscosity of air} | ||
\] | ||
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\[ | ||
\omega = \Bigg[\frac{radians}{s}\Bigg]\tag{angular frequency} | ||
\] |
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